You can change the computer name based on the user selection. We have done that before, or have multiple connection strings in the app.config, and make use of the user selection to open the appropriate connection string from there.
<connectionStrings>
<add name="Default" connectionString="....
<add name="Second" connectionString="....
...
</connectionStrings>
m_connectionStringCollection = new Hashtable();
Configuration config = ConfigurationManager.OpenExeConfiguration(ConfigurationUserLevel.None);
ConnectionStringsSection csSection = config.ConnectionStrings;
for (int i = 0; i < ConfigurationManager.ConnectionStrings.Count; i++)
{
ConnectionStringSettings cs = csSection.ConnectionStrings[i];
string connectionName = cs.Name;
m_connectionStringCollection.Add(connectionName, cs);
}